Theorems · Inductive type · general topology
Path
{X : Type u_1} → [TopologicalSpace X] → X → X → Type u_1Continuous path connecting two points x and y in a topological space
- Defined in
- Mathlib.Topology.Path
- Cited by
- 318 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by399
Results whose statement or proof uses this declaration.
- Path.transstatement and proof · cited by 54
- Path.extendstatement and proof · cited by 52
- JoinedInproof · cited by 40
- Path.reflstatement · cited by 36
- Path.symmstatement and proof · cited by 35
- curveIntegralFunstatement · cited by 33
- curveIntegralstatement · cited by 32
- Path.segmentstatement · cited by 31
- Path.extstatement and proof · cited by 30
- Joinedproof · cited by 29
- Path.Homotopicstatement and proof · cited by 28
- Path.Homotopic.Quotient.mkstatement and proof · cited by 28
Showing the 200 most cited of 399.